Find all values given the equations below such that there (a) exists exactly 1 solution (b) exists an infinite # of solutions (c) exists no solution

My work for this problem:

We have

Using Maple to get it in RREF we have:

It looks like it will always have a solution (since there is a pivot in every row). And the only way to get an infinite # of solutions would be to have a free variable. So I'm not sure what to do with this problem.